1. (04.02 MC) For an eight-hour workday, the following function represents the total number of employees that have entered a particular work building, t hours after the workday begins, where 0 s t = 8: W(t) = -0.214 - 8+3 + 9912 At what rate are employees entering the building five hours after the start of the workday? (1 point) -361.6 employees per hour 1,350 employees per hour 1,420.8 employees per hour 290 employees per hour 2. (04.02 LC) The differentiable function, S(t), gives the number of likes on a particular social media post, t minutes after it is uploaded to a particular website. Explain the meaning of S'(3) = 52. (1 point) During the first three minutes, the post received 52 likes. Fifty-two minutes after a post is uploaded, the number of likes is increasing at a rate of three likes per minute. Over 52 minutes, the post received three likes. Three minutes after a post is uploaded, the number of likes is increasing at a rate of 52 likes per minute. 3. (04.02 MC) The rate at which trash is dumped in a particular landfill, in tons per hour, is represented by the following function, where 0 s t= 8: D(t) = 100 - 35sin(0.04t-) At what rate is trash being dumped after 6.2 hours have elapsed? (1 point) 65.0193 tons/hr -1.1617 tons/hr -0.0929 tons/hr 34.9807 tons/hr4. (04.02 MC) The volume of a swimming pool being filled with water, in gallons, after t hours is modeled by the following function: V(t) = 22,500 - 10,000e-0.2t Find the rate at which the volume of water in the pool is increasing after 10 hours. (1 point) 22,770.6706 gal/hr 270.6706 gal/hr 1,353.3528 gal/hr 21,146.6472 gal/hr 5. (04.02 MC) The cost, in dollars, of producing x feet of track lighting is given by the following function: C(x) = 0.0003x3 - 0.002x2 + 0.1x + 2,400 What is the marginal cost, the instantaneous rate of change of the cost function, of 150 feet of track lighting? (1 point) 2,947.6 dollars per foot 19.65 dollars per foot 3,382.5 dollars per foot 19.75 dollars per foot